All three connect from the same page: /accounts
LinkedIn — press Connect LinkedIn Business, log in, and approve. You can publish to a company page or your personal profile (personal profiles support single images, not carousels).
YouTube — press Connect YouTube and log in with the Google account that owns your channel. The Google account must HAVE a YouTube channel. YouTube accepts video posts only.
Telegram — use the Telegram card: create a bot with Telegram's @BotFather, paste the bot token, then add the bot to your channel or group as an admin. nashir posts through that bot.
Each connected account shows as a card in Accounts with its status.